Question

solve on the interval [0,2pi)
tan(x)+sqrt3 = 0

Answer 1

ok, tan(x)+sqrt3 = 0
subtract sqrt 3 from both sides, what u get ?

Answer 2

tan(x) = -sqrt3

Answer 3

do you know for what values of x is tan x =-sqrt 3 ?

Answer 4

i have no idea hha

Answer 5

then i suggest you to remember tan values of standard angles like 0,30,60,90 degrees.
or refer to unit circle to get the angle x at which tan x = -sqrt 3

Answer 6

is that where sin/cos = -sqrt3?

Answer 7

yes, absolutely.

Answer 8

oh so 60 degrees?

Answer 9

for 60, tan 60 = +sqrt 3
look for -sqrt 3

Answer 10

300 degrees?

Answer 11

yes, thats one of the correct value of x in 4th quadrant.
there is one more in 2nd quadrant, can you find it ?

Answer 12

you can also use, \(\tan \theta = \tan(\theta -180)\)
put theta = 300 here.

Answer 13

so the answers should be given in degrees?

Answer 14

no, i think it should be given in radians, because interval [0,2pi) is in radians

Answer 15

also, could you find other angle ?

Answer 16

is it 120 degrees?

Answer 17

correct :)
now convert 120 and 300 into radians.
that will be your final answers.

Answer 18

thank you very much.. this is pretty difficult

Answer 19

welcome ^_^
with some practice, this will be a piece of cake ;)